How do you solve the system of equations $4 y = 9 x - 17$ $4y = 9x - 17$ and $9 x - 6 y = 3$ $9x - 6y = 3$ ?

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Answer 1 · 2018-03-24T10:38:14

$x = 5 and y = 7$ $x=5 and y=7$

Both equations have the same term in $x$ $x$ .

To eliminate the $x$ $x$ term, you could subtract the equations,
However, here is another option:

Isolate the $9 x$ $9x$ term in each equation.

$9 x = 6 y + 3 and 9 x = 4 y + 17$ $color(blue)(9x = 6y+3)" " and" "color(red)(9x =4y+17$

$w w w w w w w w w . 9 x = 9 x$ $color(white)(wwwwwwwww.)color(blue)(9x) =color(red)(9x)$

therefore the two right hand sides are also equal

Equate them: $6 y + 3 = 4 y + 17$ $" "color(blue)(6y+3) = color(red)(4y+17$

$w w w w w w w w w . 6 y - 4 y = 17 - 3$ $color(white)(wwwwwwwww.)6y-4y =17-3$

$w w w w w w w . w w w w . 2 y = 14$ $color(white)(wwwwwww.wwww.)2y = 14$

$color(white)(w.......www.wwwww.)y=7$

Substitute $7$ for $y$ to find the value of $x$

$color(white)(wwwwwwwww.)9x = 6(7) +3$

$color(white)(wwwwwwwww.)9x = 45$

$color(white)(wwwwwww.ww.)x =5$

How do you solve the system of equations 4y = 9x - 174y=9x−174y = 9x - 17 and 9x - 6y = 39x−6y=39x - 6y = 3?